The correct option is 2 only, as the Mysore Kingdom indeed arose from the remnants of the Vijayanagara Empire, especially after its decline in the 17th century, taking advantage of the power vacuum and expanding its influence in southern India. Statements 1 and 3 are incorrect: the Nizamat of Arcot was not directly a result of Hyderabad State but was a significant part of the Deccan territories influenced by various local powers, while the Rohilkhand Kingdom was not formed due to Ahmad Shah Durrani’s incursions, but rather established in the late 18th century by the Rohillas, a group of Afghan migrants. This distinction emphasizes the complex tapestry of political entities that emerged in India, shaped by both unique local dynamics and external invasions, key aspects of Indian historical studies relevant to the UPSC syllabus.